SOLVABILITY OF THE BOUNDARY PROBLEMS FOR THE QUASILINEAR SECOND ORDER EQUATIONS WITH PARAMETER IN THE RIGHT-HAND SIDE

А. Vorontsova, К. Buryachenko

Abstract


The paper is devoted to the problem of solvability of the first boundary value problem for a quasilinear second-order equation with a parameter in the right-hand side and a power nonlinearity of arbitrary order. Using the operator methods (inverse operator method, fixed point method), the theorem for the existence of a classical solution of a problem is proved. The methodological and theoretical aspects of the application of the obtained result for the solving of the corresponding problems are given.

Keywords


boundary value problems; quasilinear second-order equation; Green's function; fixed point; Schauder theorem

References


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